Abstract

We consider the existence, multiplicity of positive solutions for the integral boundary value problem with 𝜙-Laplacian (𝜙(𝑢(𝑡)))+𝑓(𝑡,𝑢(𝑡),𝑢(𝑡))=0, 𝑡∈[0,1], ∫𝑢(0)=10𝑢(𝑟)𝑔(𝑟)d𝑟, ∫𝑢(1)=10𝑢(𝑟)ℎ(𝑟)d𝑟, where 𝜙 is an odd, increasing homeomorphism from ℝ onto ℝ. We show that it has at least one, two, or three positive solutions under some assumptions by applying fixed point theorems. The interesting point is that the nonlinear term 𝑓 is involved with the first-order derivative explicitly.